Details

sample159.0ms

Algorithm

intervals

Results

86.0ms	147×	body	1280	valid
27.0ms	20×	body	2560	valid
18.0ms	55×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

65.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

104.0ms	(- (cos (+ x eps)) (cos x))
38.0ms	(cos (+ x eps))

simplify900.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1232
2	337
1	135
0	65

prune194.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(/ (+ x (+ x eps)) 2)
0.3b	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

25.0ms	(+ x (+ x eps))
65.0ms	(/ (+ x (+ x eps)) 2)
76.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
25.0ms	(sin (/ (+ x (+ x eps)) 2))

series267.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ x (+ x eps))
65.0ms	(/ (+ x (+ x eps)) 2)
113.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
61.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1194
1	301
0	132

prune660.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize100.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
2.4b	(sin (/ (+ x (+ x eps)) 2))
2.4b	(sin (/ (+ x (+ x eps)) 2))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

11.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
28.0ms	(sin (/ (+ x (+ x eps)) 2))
27.0ms	(sin (/ (+ x (+ x eps)) 2))
26.0ms	(sin (/ (+ x (+ x eps)) 2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
47.0ms	(sin (/ (+ x (+ x eps)) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))
43.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify3.5s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	4851
3	1071
2	308
1	121
0	57

prune377.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

localize172.0ms

Local error

Found 4 expressions with local error:

2.4b	(sin (/ (+ x (+ x eps)) 2))
2.4b	(sin (/ (+ x (+ x eps)) 2))
2.4b	(sin (/ (+ x (+ x eps)) 2))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

46.0ms	(sin (/ (+ x (+ x eps)) 2))
23.0ms	(sin (/ (+ x (+ x eps)) 2))
35.0ms	(sin (/ (+ x (+ x eps)) 2))
33.0ms	(sin (/ (+ x (+ x eps)) 2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sin (/ (+ x (+ x eps)) 2))
30.0ms	(sin (/ (+ x (+ x eps)) 2))
52.0ms	(sin (/ (+ x (+ x eps)) 2))
53.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify4.5s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
5	4077
4	1095
3	314
2	101
1	52
0	26

prune398.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.2b

regimes584.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch207.0ms

Steps

Iters	Range		Point
10	7.42116589675916e-09	160.65039477392645	0.00014597753908590782
9	-3322970397.4786234	-6367.3348759504115	-6443.306290177518

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.1s	4435×	body	1280	valid
971.0ms	637×	body	2560	valid
882.0ms	1874×	body	640	valid
217.0ms	665×	body	320	valid
99.0ms	307×	body	160	valid
8.0ms	82×	body	80	valid